Question

Go to artofstat.com, click on WebApps and open the Sampling Distribution for the Sample Mean for continuous variables (NOT discrete). Under Population Distribution select Skewed. Note the mean and standard deviation given on the graph. Which of the following statements is true?

Group of answer choices

The mean is a parameter, but the standard deviation is an estimator.

Both the mean and standard deviation are parameters,

The standard deviation is a parameter, but the mean is an estimator.

Both the mean and standard deviation are estimators,

Answer 1

Both the mean and standard deviation are parameters.

Step-by-step explanation:

The correct statement is: Both the mean and standard deviation are parameters.

In the context of statistics, a parameter is a numerical characteristic of a population. The mean and standard deviation are both parameters that describe the population distribution.

On the other hand, an estimator is a statistic that is used to estimate or approximate a population parameter. It is based on sample data. Therefore, the mean and standard deviation are not estimators, but rather parameters.

Answer 2

The statement that is true of mean and standard deviation is A. The mean is a parameter, but the standard deviation is an estimator.

How are mean and standard deviation different ?

In a skewed population distribution, the mean is still a parameter, but the standard deviation is an estimator. This is because the mean is a characteristic of the entire population, while the standard deviation is a measure of the variability of a sample.

Since a sample is only a subset of the population, the standard deviation calculated from a sample will only estimate the true standard deviation of the population.